Question

A triangle with an area of $10$ square meters has a base of $4$ meters. A similar triangle has an area of $90$ square meters. What is the height of the larger triangle?

Answer 1

Find the height of larger triangle.

Given,

A triangle with an area of $10$ square meter has a base of $4$ meters.

A similar triangle has an area of $90$ square meters.

Since we know the area of triangle = $\frac{1}{2}\times \mathrm{base}\times \mathrm{height}$

So, height of triangle is

$$\begin{gathered} =\frac{2\times Area}{base} \\ =\frac{2\times 10}{4} \\ =5\mathrm{meters} \end{gathered}$$

Also, we know that for similarity of triangles.

$\Rightarrow \frac{Areaofsimilartriangle}{Areaoforiginaltriangle}=\frac{{(heightofsimilartriangle)}^2}{{(heightoforiginaltriangle)}^2}$

So, the height of similar triangle is

$$\begin{gathered} \Rightarrow \frac{90}{10}=\frac{{(heightofsimilartriangle)}^2}{{\left(5\right)}^2} \\ \Rightarrow heightofsimilartriangle=15meters. \end{gathered}$$

Hence, the height of triangle is $15\mathrm{meters}.$